<HTML>
<BODY BGCOLOR="white">
<PRE>
<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.transform;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.FunctionUtils;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.25"></a>
<FONT color="green">026</FONT>    <a name="line.26"></a>
<FONT color="green">027</FONT>    /**<a name="line.27"></a>
<FONT color="green">028</FONT>     * Implements the &lt;a href="http://www.archive.chipcenter.com/dsp/DSP000517F1.html"&gt;Fast Hadamard Transform&lt;/a&gt; (FHT).<a name="line.28"></a>
<FONT color="green">029</FONT>     * Transformation of an input vector x to the output vector y.<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * In addition to transformation of real vectors, the Hadamard transform can<a name="line.31"></a>
<FONT color="green">032</FONT>     * transform integer vectors into integer vectors. However, this integer transform<a name="line.32"></a>
<FONT color="green">033</FONT>     * cannot be inverted directly. Due to a scaling factor it may lead to rational results.<a name="line.33"></a>
<FONT color="green">034</FONT>     * As an example, the inverse transform of integer vector (0, 1, 0, 1) is rational<a name="line.34"></a>
<FONT color="green">035</FONT>     * vector (1/2, -1/2, 0, 0).<a name="line.35"></a>
<FONT color="green">036</FONT>     *<a name="line.36"></a>
<FONT color="green">037</FONT>     * @version $Id: FastHadamardTransformer.java 1385310 2012-09-16 16:32:10Z tn $<a name="line.37"></a>
<FONT color="green">038</FONT>     * @since 2.0<a name="line.38"></a>
<FONT color="green">039</FONT>     */<a name="line.39"></a>
<FONT color="green">040</FONT>    public class FastHadamardTransformer implements RealTransformer, Serializable {<a name="line.40"></a>
<FONT color="green">041</FONT>    <a name="line.41"></a>
<FONT color="green">042</FONT>        /** Serializable version identifier. */<a name="line.42"></a>
<FONT color="green">043</FONT>        static final long serialVersionUID = 20120211L;<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>        /**<a name="line.45"></a>
<FONT color="green">046</FONT>         * {@inheritDoc}<a name="line.46"></a>
<FONT color="green">047</FONT>         *<a name="line.47"></a>
<FONT color="green">048</FONT>         * @throws MathIllegalArgumentException if the length of the data array is<a name="line.48"></a>
<FONT color="green">049</FONT>         * not a power of two<a name="line.49"></a>
<FONT color="green">050</FONT>         */<a name="line.50"></a>
<FONT color="green">051</FONT>        public double[] transform(final double[] f, final TransformType type) {<a name="line.51"></a>
<FONT color="green">052</FONT>            if (type == TransformType.FORWARD) {<a name="line.52"></a>
<FONT color="green">053</FONT>                return fht(f);<a name="line.53"></a>
<FONT color="green">054</FONT>            }<a name="line.54"></a>
<FONT color="green">055</FONT>            return TransformUtils.scaleArray(fht(f), 1.0 / f.length);<a name="line.55"></a>
<FONT color="green">056</FONT>        }<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>        /**<a name="line.58"></a>
<FONT color="green">059</FONT>         * {@inheritDoc}<a name="line.59"></a>
<FONT color="green">060</FONT>         *<a name="line.60"></a>
<FONT color="green">061</FONT>         * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException<a name="line.61"></a>
<FONT color="green">062</FONT>         *   if the lower bound is greater than, or equal to the upper bound<a name="line.62"></a>
<FONT color="green">063</FONT>         * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException<a name="line.63"></a>
<FONT color="green">064</FONT>         *   if the number of sample points is negative<a name="line.64"></a>
<FONT color="green">065</FONT>         * @throws MathIllegalArgumentException if the number of sample points is not a power of two<a name="line.65"></a>
<FONT color="green">066</FONT>         */<a name="line.66"></a>
<FONT color="green">067</FONT>        public double[] transform(final UnivariateFunction f,<a name="line.67"></a>
<FONT color="green">068</FONT>            final double min, final double max, final int n,<a name="line.68"></a>
<FONT color="green">069</FONT>            final TransformType type) {<a name="line.69"></a>
<FONT color="green">070</FONT>    <a name="line.70"></a>
<FONT color="green">071</FONT>            return transform(FunctionUtils.sample(f, min, max, n), type);<a name="line.71"></a>
<FONT color="green">072</FONT>        }<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>        /**<a name="line.74"></a>
<FONT color="green">075</FONT>         * Returns the forward transform of the specified integer data set.The<a name="line.75"></a>
<FONT color="green">076</FONT>         * integer transform cannot be inverted directly, due to a scaling factor<a name="line.76"></a>
<FONT color="green">077</FONT>         * which may lead to double results.<a name="line.77"></a>
<FONT color="green">078</FONT>         *<a name="line.78"></a>
<FONT color="green">079</FONT>         * @param f the integer data array to be transformed (signal)<a name="line.79"></a>
<FONT color="green">080</FONT>         * @return the integer transformed array (spectrum)<a name="line.80"></a>
<FONT color="green">081</FONT>         * @throws MathIllegalArgumentException if the length of the data array is not a power of two<a name="line.81"></a>
<FONT color="green">082</FONT>         */<a name="line.82"></a>
<FONT color="green">083</FONT>        public int[] transform(final int[] f) {<a name="line.83"></a>
<FONT color="green">084</FONT>            return fht(f);<a name="line.84"></a>
<FONT color="green">085</FONT>        }<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /**<a name="line.87"></a>
<FONT color="green">088</FONT>         * The FHT (Fast Hadamard Transformation) which uses only subtraction and<a name="line.88"></a>
<FONT color="green">089</FONT>         * addition. Requires {@code N * log2(N) = n * 2^n} additions.<a name="line.89"></a>
<FONT color="green">090</FONT>         *<a name="line.90"></a>
<FONT color="green">091</FONT>         * &lt;h3&gt;Short Table of manual calculation for N=8&lt;/h3&gt;<a name="line.91"></a>
<FONT color="green">092</FONT>         * &lt;ol&gt;<a name="line.92"></a>
<FONT color="green">093</FONT>         * &lt;li&gt;&lt;b&gt;x&lt;/b&gt; is the input vector to be transformed,&lt;/li&gt;<a name="line.93"></a>
<FONT color="green">094</FONT>         * &lt;li&gt;&lt;b&gt;y&lt;/b&gt; is the output vector (Fast Hadamard transform of &lt;b&gt;x&lt;/b&gt;),&lt;/li&gt;<a name="line.94"></a>
<FONT color="green">095</FONT>         * &lt;li&gt;a and b are helper rows.&lt;/li&gt;<a name="line.95"></a>
<FONT color="green">096</FONT>         * &lt;/ol&gt;<a name="line.96"></a>
<FONT color="green">097</FONT>         * &lt;table align="center" border="1" cellpadding="3"&gt;<a name="line.97"></a>
<FONT color="green">098</FONT>         * &lt;tbody align="center"&gt;<a name="line.98"></a>
<FONT color="green">099</FONT>         * &lt;tr&gt;<a name="line.99"></a>
<FONT color="green">100</FONT>         *     &lt;th&gt;x&lt;/th&gt;<a name="line.100"></a>
<FONT color="green">101</FONT>         *     &lt;th&gt;a&lt;/th&gt;<a name="line.101"></a>
<FONT color="green">102</FONT>         *     &lt;th&gt;b&lt;/th&gt;<a name="line.102"></a>
<FONT color="green">103</FONT>         *     &lt;th&gt;y&lt;/th&gt;<a name="line.103"></a>
<FONT color="green">104</FONT>         * &lt;/tr&gt;<a name="line.104"></a>
<FONT color="green">105</FONT>         * &lt;tr&gt;<a name="line.105"></a>
<FONT color="green">106</FONT>         *     &lt;th&gt;x&lt;sub&gt;0&lt;/sub&gt;&lt;/th&gt;<a name="line.106"></a>
<FONT color="green">107</FONT>         *     &lt;td&gt;a&lt;sub&gt;0&lt;/sub&gt; = x&lt;sub&gt;0&lt;/sub&gt; + x&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;<a name="line.107"></a>
<FONT color="green">108</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;0&lt;/sub&gt; + a&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;<a name="line.108"></a>
<FONT color="green">109</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;0&lt;/sub &gt;+ b&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;<a name="line.109"></a>
<FONT color="green">110</FONT>         * &lt;/tr&gt;<a name="line.110"></a>
<FONT color="green">111</FONT>         * &lt;tr&gt;<a name="line.111"></a>
<FONT color="green">112</FONT>         *     &lt;th&gt;x&lt;sub&gt;1&lt;/sub&gt;&lt;/th&gt;<a name="line.112"></a>
<FONT color="green">113</FONT>         *     &lt;td&gt;a&lt;sub&gt;1&lt;/sub&gt; = x&lt;sub&gt;2&lt;/sub&gt; + x&lt;sub&gt;3&lt;/sub&gt;&lt;/td&gt;<a name="line.113"></a>
<FONT color="green">114</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;2&lt;/sub&gt; + a&lt;sub&gt;3&lt;/sub&gt;&lt;/td&gt;<a name="line.114"></a>
<FONT color="green">115</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;2&lt;/sub&gt; + b&lt;sub&gt;3&lt;/sub&gt;&lt;/td&gt;<a name="line.115"></a>
<FONT color="green">116</FONT>         * &lt;/tr&gt;<a name="line.116"></a>
<FONT color="green">117</FONT>         * &lt;tr&gt;<a name="line.117"></a>
<FONT color="green">118</FONT>         *     &lt;th&gt;x&lt;sub&gt;2&lt;/sub&gt;&lt;/th&gt;<a name="line.118"></a>
<FONT color="green">119</FONT>         *     &lt;td&gt;a&lt;sub&gt;2&lt;/sub&gt; = x&lt;sub&gt;4&lt;/sub&gt; + x&lt;sub&gt;5&lt;/sub&gt;&lt;/td&gt;<a name="line.119"></a>
<FONT color="green">120</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;4&lt;/sub&gt; + a&lt;sub&gt;5&lt;/sub&gt;&lt;/td&gt;<a name="line.120"></a>
<FONT color="green">121</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;4&lt;/sub&gt; + b&lt;sub&gt;5&lt;/sub&gt;&lt;/td&gt;<a name="line.121"></a>
<FONT color="green">122</FONT>         * &lt;/tr&gt;<a name="line.122"></a>
<FONT color="green">123</FONT>         * &lt;tr&gt;<a name="line.123"></a>
<FONT color="green">124</FONT>         *     &lt;th&gt;x&lt;sub&gt;3&lt;/sub&gt;&lt;/th&gt;<a name="line.124"></a>
<FONT color="green">125</FONT>         *     &lt;td&gt;a&lt;sub&gt;3&lt;/sub&gt; = x&lt;sub&gt;6&lt;/sub&gt; + x&lt;sub&gt;7&lt;/sub&gt;&lt;/td&gt;<a name="line.125"></a>
<FONT color="green">126</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;6&lt;/sub&gt; + a&lt;sub&gt;7&lt;/sub&gt;&lt;/td&gt;<a name="line.126"></a>
<FONT color="green">127</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;6&lt;/sub&gt; + b&lt;sub&gt;7&lt;/sub&gt;&lt;/td&gt;<a name="line.127"></a>
<FONT color="green">128</FONT>         * &lt;/tr&gt;<a name="line.128"></a>
<FONT color="green">129</FONT>         * &lt;tr&gt;<a name="line.129"></a>
<FONT color="green">130</FONT>         *     &lt;th&gt;x&lt;sub&gt;4&lt;/sub&gt;&lt;/th&gt;<a name="line.130"></a>
<FONT color="green">131</FONT>         *     &lt;td&gt;a&lt;sub&gt;0&lt;/sub&gt; = x&lt;sub&gt;0&lt;/sub&gt; - x&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;<a name="line.131"></a>
<FONT color="green">132</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;0&lt;/sub&gt; - a&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;<a name="line.132"></a>
<FONT color="green">133</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;0&lt;/sub&gt; - b&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;<a name="line.133"></a>
<FONT color="green">134</FONT>         * &lt;/tr&gt;<a name="line.134"></a>
<FONT color="green">135</FONT>         * &lt;tr&gt;<a name="line.135"></a>
<FONT color="green">136</FONT>         *     &lt;th&gt;x&lt;sub&gt;5&lt;/sub&gt;&lt;/th&gt;<a name="line.136"></a>
<FONT color="green">137</FONT>         *     &lt;td&gt;a&lt;sub&gt;1&lt;/sub&gt; = x&lt;sub&gt;2&lt;/sub&gt; - x&lt;sub&gt;3&lt;/sub&gt;&lt;/td&gt;<a name="line.137"></a>
<FONT color="green">138</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;2&lt;/sub&gt; - a&lt;sub&gt;3&lt;/sub&gt;&lt;/td&gt;<a name="line.138"></a>
<FONT color="green">139</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;2&lt;/sub&gt; - b&lt;sub&gt;3&lt;/sub&gt;&lt;/td&gt;<a name="line.139"></a>
<FONT color="green">140</FONT>         * &lt;/tr&gt;<a name="line.140"></a>
<FONT color="green">141</FONT>         * &lt;tr&gt;<a name="line.141"></a>
<FONT color="green">142</FONT>         *     &lt;th&gt;x&lt;sub&gt;6&lt;/sub&gt;&lt;/th&gt;<a name="line.142"></a>
<FONT color="green">143</FONT>         *     &lt;td&gt;a&lt;sub&gt;2&lt;/sub&gt; = x&lt;sub&gt;4&lt;/sub&gt; - x&lt;sub&gt;5&lt;/sub&gt;&lt;/td&gt;<a name="line.143"></a>
<FONT color="green">144</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;4&lt;/sub&gt; - a&lt;sub&gt;5&lt;/sub&gt;&lt;/td&gt;<a name="line.144"></a>
<FONT color="green">145</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;4&lt;/sub&gt; - b&lt;sub&gt;5&lt;/sub&gt;&lt;/td&gt;<a name="line.145"></a>
<FONT color="green">146</FONT>         * &lt;/tr&gt;<a name="line.146"></a>
<FONT color="green">147</FONT>         * &lt;tr&gt;<a name="line.147"></a>
<FONT color="green">148</FONT>         *     &lt;th&gt;x&lt;sub&gt;7&lt;/sub&gt;&lt;/th&gt;<a name="line.148"></a>
<FONT color="green">149</FONT>         *     &lt;td&gt;a&lt;sub&gt;3&lt;/sub&gt; = x&lt;sub&gt;6&lt;/sub&gt; - x&lt;sub&gt;7&lt;/sub&gt;&lt;/td&gt;<a name="line.149"></a>
<FONT color="green">150</FONT>         *     &lt;td&gt;b&lt;sub&gt;0&lt;/sub&gt; = a&lt;sub&gt;6&lt;/sub&gt; - a&lt;sub&gt;7&lt;/sub&gt;&lt;/td&gt;<a name="line.150"></a>
<FONT color="green">151</FONT>         *     &lt;td&gt;y&lt;sub&gt;0&lt;/sub&gt; = b&lt;sub&gt;6&lt;/sub&gt; - b&lt;sub&gt;7&lt;/sub&gt;&lt;/td&gt;<a name="line.151"></a>
<FONT color="green">152</FONT>         * &lt;/tr&gt;<a name="line.152"></a>
<FONT color="green">153</FONT>         * &lt;/tbody&gt;<a name="line.153"></a>
<FONT color="green">154</FONT>         * &lt;/table&gt;<a name="line.154"></a>
<FONT color="green">155</FONT>         *<a name="line.155"></a>
<FONT color="green">156</FONT>         * &lt;h3&gt;How it works&lt;/h3&gt;<a name="line.156"></a>
<FONT color="green">157</FONT>         * &lt;ol&gt;<a name="line.157"></a>
<FONT color="green">158</FONT>         * &lt;li&gt;Construct a matrix with {@code N} rows and {@code n + 1} columns,<a name="line.158"></a>
<FONT color="green">159</FONT>         * {@code hadm[n+1][N]}.&lt;br/&gt;<a name="line.159"></a>
<FONT color="green">160</FONT>         * &lt;em&gt;(If I use [x][y] it always means [row-offset][column-offset] of a<a name="line.160"></a>
<FONT color="green">161</FONT>         * Matrix with n rows and m columns. Its entries go from M[0][0]<a name="line.161"></a>
<FONT color="green">162</FONT>         * to M[n][N])&lt;/em&gt;&lt;/li&gt;<a name="line.162"></a>
<FONT color="green">163</FONT>         * &lt;li&gt;Place the input vector {@code x[N]} in the first column of the<a name="line.163"></a>
<FONT color="green">164</FONT>         * matrix {@code hadm}.&lt;/li&gt;<a name="line.164"></a>
<FONT color="green">165</FONT>         * &lt;li&gt;The entries of the submatrix {@code D_top} are calculated as follows<a name="line.165"></a>
<FONT color="green">166</FONT>         *     &lt;ul&gt;<a name="line.166"></a>
<FONT color="green">167</FONT>         *         &lt;li&gt;{@code D_top} goes from entry {@code [0][1]} to<a name="line.167"></a>
<FONT color="green">168</FONT>         *         {@code [N / 2 - 1][n + 1]},&lt;/li&gt;<a name="line.168"></a>
<FONT color="green">169</FONT>         *         &lt;li&gt;the columns of {@code D_top} are the pairwise mutually<a name="line.169"></a>
<FONT color="green">170</FONT>         *         exclusive sums of the previous column.&lt;/li&gt;<a name="line.170"></a>
<FONT color="green">171</FONT>         *     &lt;/ul&gt;<a name="line.171"></a>
<FONT color="green">172</FONT>         * &lt;/li&gt;<a name="line.172"></a>
<FONT color="green">173</FONT>         * &lt;li&gt;The entries of the submatrix {@code D_bottom} are calculated as<a name="line.173"></a>
<FONT color="green">174</FONT>         * follows<a name="line.174"></a>
<FONT color="green">175</FONT>         *     &lt;ul&gt;<a name="line.175"></a>
<FONT color="green">176</FONT>         *         &lt;li&gt;{@code D_bottom} goes from entry {@code [N / 2][1]} to<a name="line.176"></a>
<FONT color="green">177</FONT>         *         {@code [N][n + 1]},&lt;/li&gt;<a name="line.177"></a>
<FONT color="green">178</FONT>         *         &lt;li&gt;the columns of {@code D_bottom} are the pairwise differences<a name="line.178"></a>
<FONT color="green">179</FONT>         *         of the previous column.&lt;/li&gt;<a name="line.179"></a>
<FONT color="green">180</FONT>         *     &lt;/ul&gt;<a name="line.180"></a>
<FONT color="green">181</FONT>         * &lt;/li&gt;<a name="line.181"></a>
<FONT color="green">182</FONT>         * &lt;li&gt;The consputation of {@code D_top} and {@code D_bottom} are best<a name="line.182"></a>
<FONT color="green">183</FONT>         * understood with the above example (for {@code N = 8}).<a name="line.183"></a>
<FONT color="green">184</FONT>         * &lt;li&gt;The output vector {@code y} is now in the last column of<a name="line.184"></a>
<FONT color="green">185</FONT>         * {@code hadm}.&lt;/li&gt;<a name="line.185"></a>
<FONT color="green">186</FONT>         * &lt;li&gt;&lt;em&gt;Algorithm from &lt;a href="http://www.archive.chipcenter.com/dsp/DSP000517F1.html"&gt;chipcenter&lt;/a&gt;.&lt;/em&gt;&lt;/li&gt;<a name="line.186"></a>
<FONT color="green">187</FONT>         * &lt;/ol&gt;<a name="line.187"></a>
<FONT color="green">188</FONT>         * &lt;h3&gt;Visually&lt;/h3&gt;<a name="line.188"></a>
<FONT color="green">189</FONT>         * &lt;table border="1" align="center" cellpadding="3"&gt;<a name="line.189"></a>
<FONT color="green">190</FONT>         * &lt;tbody align="center"&gt;<a name="line.190"></a>
<FONT color="green">191</FONT>         * &lt;tr&gt;<a name="line.191"></a>
<FONT color="green">192</FONT>         *     &lt;td&gt;&lt;/td&gt;&lt;th&gt;0&lt;/th&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;2&lt;/th&gt;&lt;th&gt;3&lt;/th&gt;<a name="line.192"></a>
<FONT color="green">193</FONT>         *     &lt;th&gt;&amp;hellip;&lt;/th&gt;<a name="line.193"></a>
<FONT color="green">194</FONT>         *     &lt;th&gt;n + 1&lt;/th&gt;<a name="line.194"></a>
<FONT color="green">195</FONT>         * &lt;/tr&gt;<a name="line.195"></a>
<FONT color="green">196</FONT>         * &lt;tr&gt;<a name="line.196"></a>
<FONT color="green">197</FONT>         *     &lt;th&gt;0&lt;/th&gt;<a name="line.197"></a>
<FONT color="green">198</FONT>         *     &lt;td&gt;x&lt;sub&gt;0&lt;/sub&gt;&lt;/td&gt;<a name="line.198"></a>
<FONT color="green">199</FONT>         *     &lt;td colspan="5" rowspan="5" align="center" valign="middle"&gt;<a name="line.199"></a>
<FONT color="green">200</FONT>         *         &amp;uarr;&lt;br/&gt;<a name="line.200"></a>
<FONT color="green">201</FONT>         *         &amp;larr; D&lt;sub&gt;top&lt;/sub&gt; &amp;rarr;&lt;br/&gt;<a name="line.201"></a>
<FONT color="green">202</FONT>         *         &amp;darr;<a name="line.202"></a>
<FONT color="green">203</FONT>         *     &lt;/td&gt;<a name="line.203"></a>
<FONT color="green">204</FONT>         * &lt;/tr&gt;<a name="line.204"></a>
<FONT color="green">205</FONT>         * &lt;tr&gt;&lt;th&gt;1&lt;/th&gt;&lt;td&gt;x&lt;sub&gt;1&lt;/sub&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.205"></a>
<FONT color="green">206</FONT>         * &lt;tr&gt;&lt;th&gt;2&lt;/th&gt;&lt;td&gt;x&lt;sub&gt;2&lt;/sub&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.206"></a>
<FONT color="green">207</FONT>         * &lt;tr&gt;&lt;th&gt;&amp;hellip;&lt;/th&gt;&lt;td&gt;&amp;hellip;&lt;/td&gt;&lt;/tr&gt;<a name="line.207"></a>
<FONT color="green">208</FONT>         * &lt;tr&gt;&lt;th&gt;N / 2 - 1&lt;/th&gt;&lt;td&gt;x&lt;sub&gt;N/2-1&lt;/sub&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.208"></a>
<FONT color="green">209</FONT>         * &lt;tr&gt;<a name="line.209"></a>
<FONT color="green">210</FONT>         *     &lt;th&gt;N / 2&lt;/th&gt;<a name="line.210"></a>
<FONT color="green">211</FONT>         *     &lt;td&gt;x&lt;sub&gt;N/2&lt;/sub&gt;&lt;/td&gt;<a name="line.211"></a>
<FONT color="green">212</FONT>         *     &lt;td colspan="5" rowspan="5" align="center" valign="middle"&gt;<a name="line.212"></a>
<FONT color="green">213</FONT>         *         &amp;uarr;&lt;br/&gt;<a name="line.213"></a>
<FONT color="green">214</FONT>         *         &amp;larr; D&lt;sub&gt;bottom&lt;/sub&gt; &amp;rarr;&lt;br/&gt;<a name="line.214"></a>
<FONT color="green">215</FONT>         *         &amp;darr;<a name="line.215"></a>
<FONT color="green">216</FONT>         *     &lt;/td&gt;<a name="line.216"></a>
<FONT color="green">217</FONT>         * &lt;/tr&gt;<a name="line.217"></a>
<FONT color="green">218</FONT>         * &lt;tr&gt;&lt;th&gt;N / 2 + 1&lt;/th&gt;&lt;td&gt;x&lt;sub&gt;N/2+1&lt;/sub&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.218"></a>
<FONT color="green">219</FONT>         * &lt;tr&gt;&lt;th&gt;N / 2 + 2&lt;/th&gt;&lt;td&gt;x&lt;sub&gt;N/2+2&lt;/sub&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.219"></a>
<FONT color="green">220</FONT>         * &lt;tr&gt;&lt;th&gt;&amp;hellip;&lt;/th&gt;&lt;td&gt;&amp;hellip;&lt;/td&gt;&lt;/tr&gt;<a name="line.220"></a>
<FONT color="green">221</FONT>         * &lt;tr&gt;&lt;th&gt;N&lt;/th&gt;&lt;td&gt;x&lt;sub&gt;N&lt;/sub&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.221"></a>
<FONT color="green">222</FONT>         * &lt;/tbody&gt;<a name="line.222"></a>
<FONT color="green">223</FONT>         * &lt;/table&gt;<a name="line.223"></a>
<FONT color="green">224</FONT>         *<a name="line.224"></a>
<FONT color="green">225</FONT>         * @param x the real data array to be transformed<a name="line.225"></a>
<FONT color="green">226</FONT>         * @return the real transformed array, {@code y}<a name="line.226"></a>
<FONT color="green">227</FONT>         * @throws MathIllegalArgumentException if the length of the data array is not a power of two<a name="line.227"></a>
<FONT color="green">228</FONT>         */<a name="line.228"></a>
<FONT color="green">229</FONT>        protected double[] fht(double[] x) throws MathIllegalArgumentException {<a name="line.229"></a>
<FONT color="green">230</FONT>    <a name="line.230"></a>
<FONT color="green">231</FONT>            final int n     = x.length;<a name="line.231"></a>
<FONT color="green">232</FONT>            final int halfN = n / 2;<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>            if (!ArithmeticUtils.isPowerOfTwo(n)) {<a name="line.234"></a>
<FONT color="green">235</FONT>                throw new MathIllegalArgumentException(<a name="line.235"></a>
<FONT color="green">236</FONT>                        LocalizedFormats.NOT_POWER_OF_TWO,<a name="line.236"></a>
<FONT color="green">237</FONT>                        Integer.valueOf(n));<a name="line.237"></a>
<FONT color="green">238</FONT>            }<a name="line.238"></a>
<FONT color="green">239</FONT>    <a name="line.239"></a>
<FONT color="green">240</FONT>            /*<a name="line.240"></a>
<FONT color="green">241</FONT>             * Instead of creating a matrix with p+1 columns and n rows, we use two<a name="line.241"></a>
<FONT color="green">242</FONT>             * one dimension arrays which we are used in an alternating way.<a name="line.242"></a>
<FONT color="green">243</FONT>             */<a name="line.243"></a>
<FONT color="green">244</FONT>            double[] yPrevious = new double[n];<a name="line.244"></a>
<FONT color="green">245</FONT>            double[] yCurrent  = x.clone();<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>            // iterate from left to right (column)<a name="line.247"></a>
<FONT color="green">248</FONT>            for (int j = 1; j &lt; n; j &lt;&lt;= 1) {<a name="line.248"></a>
<FONT color="green">249</FONT>    <a name="line.249"></a>
<FONT color="green">250</FONT>                // switch columns<a name="line.250"></a>
<FONT color="green">251</FONT>                final double[] yTmp = yCurrent;<a name="line.251"></a>
<FONT color="green">252</FONT>                yCurrent  = yPrevious;<a name="line.252"></a>
<FONT color="green">253</FONT>                yPrevious = yTmp;<a name="line.253"></a>
<FONT color="green">254</FONT>    <a name="line.254"></a>
<FONT color="green">255</FONT>                // iterate from top to bottom (row)<a name="line.255"></a>
<FONT color="green">256</FONT>                for (int i = 0; i &lt; halfN; ++i) {<a name="line.256"></a>
<FONT color="green">257</FONT>                    // Dtop: the top part works with addition<a name="line.257"></a>
<FONT color="green">258</FONT>                    final int twoI = 2 * i;<a name="line.258"></a>
<FONT color="green">259</FONT>                    yCurrent[i] = yPrevious[twoI] + yPrevious[twoI + 1];<a name="line.259"></a>
<FONT color="green">260</FONT>                }<a name="line.260"></a>
<FONT color="green">261</FONT>                for (int i = halfN; i &lt; n; ++i) {<a name="line.261"></a>
<FONT color="green">262</FONT>                    // Dbottom: the bottom part works with subtraction<a name="line.262"></a>
<FONT color="green">263</FONT>                    final int twoI = 2 * i;<a name="line.263"></a>
<FONT color="green">264</FONT>                    yCurrent[i] = yPrevious[twoI - n] - yPrevious[twoI - n + 1];<a name="line.264"></a>
<FONT color="green">265</FONT>                }<a name="line.265"></a>
<FONT color="green">266</FONT>            }<a name="line.266"></a>
<FONT color="green">267</FONT>    <a name="line.267"></a>
<FONT color="green">268</FONT>            return yCurrent;<a name="line.268"></a>
<FONT color="green">269</FONT>    <a name="line.269"></a>
<FONT color="green">270</FONT>        }<a name="line.270"></a>
<FONT color="green">271</FONT>    <a name="line.271"></a>
<FONT color="green">272</FONT>        /**<a name="line.272"></a>
<FONT color="green">273</FONT>         * Returns the forward transform of the specified integer data set. The FHT<a name="line.273"></a>
<FONT color="green">274</FONT>         * (Fast Hadamard Transform) uses only subtraction and addition.<a name="line.274"></a>
<FONT color="green">275</FONT>         *<a name="line.275"></a>
<FONT color="green">276</FONT>         * @param x the integer data array to be transformed<a name="line.276"></a>
<FONT color="green">277</FONT>         * @return the integer transformed array, {@code y}<a name="line.277"></a>
<FONT color="green">278</FONT>         * @throws MathIllegalArgumentException if the length of the data array is not a power of two<a name="line.278"></a>
<FONT color="green">279</FONT>         */<a name="line.279"></a>
<FONT color="green">280</FONT>        protected int[] fht(int[] x) throws MathIllegalArgumentException {<a name="line.280"></a>
<FONT color="green">281</FONT>    <a name="line.281"></a>
<FONT color="green">282</FONT>            final int n     = x.length;<a name="line.282"></a>
<FONT color="green">283</FONT>            final int halfN = n / 2;<a name="line.283"></a>
<FONT color="green">284</FONT>    <a name="line.284"></a>
<FONT color="green">285</FONT>            if (!ArithmeticUtils.isPowerOfTwo(n)) {<a name="line.285"></a>
<FONT color="green">286</FONT>                throw new MathIllegalArgumentException(<a name="line.286"></a>
<FONT color="green">287</FONT>                        LocalizedFormats.NOT_POWER_OF_TWO,<a name="line.287"></a>
<FONT color="green">288</FONT>                        Integer.valueOf(n));<a name="line.288"></a>
<FONT color="green">289</FONT>            }<a name="line.289"></a>
<FONT color="green">290</FONT>    <a name="line.290"></a>
<FONT color="green">291</FONT>            /*<a name="line.291"></a>
<FONT color="green">292</FONT>             * Instead of creating a matrix with p+1 columns and n rows, we use two<a name="line.292"></a>
<FONT color="green">293</FONT>             * one dimension arrays which we are used in an alternating way.<a name="line.293"></a>
<FONT color="green">294</FONT>             */<a name="line.294"></a>
<FONT color="green">295</FONT>            int[] yPrevious = new int[n];<a name="line.295"></a>
<FONT color="green">296</FONT>            int[] yCurrent  = x.clone();<a name="line.296"></a>
<FONT color="green">297</FONT>    <a name="line.297"></a>
<FONT color="green">298</FONT>            // iterate from left to right (column)<a name="line.298"></a>
<FONT color="green">299</FONT>            for (int j = 1; j &lt; n; j &lt;&lt;= 1) {<a name="line.299"></a>
<FONT color="green">300</FONT>    <a name="line.300"></a>
<FONT color="green">301</FONT>                // switch columns<a name="line.301"></a>
<FONT color="green">302</FONT>                final int[] yTmp = yCurrent;<a name="line.302"></a>
<FONT color="green">303</FONT>                yCurrent  = yPrevious;<a name="line.303"></a>
<FONT color="green">304</FONT>                yPrevious = yTmp;<a name="line.304"></a>
<FONT color="green">305</FONT>    <a name="line.305"></a>
<FONT color="green">306</FONT>                // iterate from top to bottom (row)<a name="line.306"></a>
<FONT color="green">307</FONT>                for (int i = 0; i &lt; halfN; ++i) {<a name="line.307"></a>
<FONT color="green">308</FONT>                    // Dtop: the top part works with addition<a name="line.308"></a>
<FONT color="green">309</FONT>                    final int twoI = 2 * i;<a name="line.309"></a>
<FONT color="green">310</FONT>                    yCurrent[i] = yPrevious[twoI] + yPrevious[twoI + 1];<a name="line.310"></a>
<FONT color="green">311</FONT>                }<a name="line.311"></a>
<FONT color="green">312</FONT>                for (int i = halfN; i &lt; n; ++i) {<a name="line.312"></a>
<FONT color="green">313</FONT>                    // Dbottom: the bottom part works with subtraction<a name="line.313"></a>
<FONT color="green">314</FONT>                    final int twoI = 2 * i;<a name="line.314"></a>
<FONT color="green">315</FONT>                    yCurrent[i] = yPrevious[twoI - n] - yPrevious[twoI - n + 1];<a name="line.315"></a>
<FONT color="green">316</FONT>                }<a name="line.316"></a>
<FONT color="green">317</FONT>            }<a name="line.317"></a>
<FONT color="green">318</FONT>    <a name="line.318"></a>
<FONT color="green">319</FONT>            // return the last computed output vector y<a name="line.319"></a>
<FONT color="green">320</FONT>            return yCurrent;<a name="line.320"></a>
<FONT color="green">321</FONT>    <a name="line.321"></a>
<FONT color="green">322</FONT>        }<a name="line.322"></a>
<FONT color="green">323</FONT>    <a name="line.323"></a>
<FONT color="green">324</FONT>    }<a name="line.324"></a>




























































</PRE>
</BODY>
</HTML>
